There is a letter in the Louisiana State Museum, RECORD GROUP 35, George Smith Collection about the son, showing that he is alive in 1859. The collection description notes a letter from Charles Etienne Arthur Gayarre [1805 - 1895] to his acknowledged natural son Charles Nicolas Arthur Gayarre, f.m.c. [b.1825] AKA Charles Gayarre, Jr., challenging the latter's attempt to pass for white (1859).
Source: Susan Tucker

Charles Gayarre did have a son, when he was 21, with a young octaroon slave girl in his household, Delphine LeMaitre. I found that this son lived in New Orleans and died 28 Mar 1906 and is buried in St. Louis Cemetery No. 3 (although his birth date is incorrectly inscribed there as 1830).
Source: Jarrell Robinson